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The equation of Line 1 is y=-2x + 7. Line 2 passesthrough the points (2, 3) and (4, 4). Which statementis true about Line 1 and Line 2?Line 1 and Line 2 are perpendicularO Line 1 is longer than Line 2Line 1 has the same y-intercept as Line 2Line 1 and Line 2 are parallel



Answer :

SOLUTION

Line 1 is given as

[tex]y=-2x+7[/tex]

let's find the equation of line 2, it passes through points (2, 3) and (4, 4)

The slope is

[tex]\begin{gathered} m=\frac{4-3}{4-2} \\ m=\frac{1}{2} \end{gathered}[/tex]

The slope of line 2 is 1/2

If the two lines are perpendicular, then the product of their slope will be = -1, that is

[tex]\begin{gathered} m_1m_2=-1 \\ slope\text{ of line 1 m}_1=-2 \\ slope\text{ of line 2, m}_2=\frac{1}{2} \\ -2\times\frac{1}{2}=\frac{-2}{2}=-1 \\ \end{gathered}[/tex]

Since the product of their slope = -1

Hence Line 1 and Line 2 are perpendicular

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